Misfire on idle

recently took my car for an mot and it failed emissions test. the car has a very slight misfire on idle all emissions passed apart from the idle test. as it misses there is slight movement in engine nothing severe tho. misfire vanishes as soon as you touch throttle. just need get the MOT sorted lol don't care about misfire just hate having no car although be nice to cure it

Recently had new plugs and new coil pack which I changed again incase the new one was faulty. sometimes the engine management light comes on but goes off again. had a few issues with smoke. looks like oil based smoke as its a little blue at high revs or should I say under load (whilst going along)
had tech 2 on it no codes stored...... its doing my head in cant find the cause.

took rocker cover off when I did an oil change a few month ago and it was clogged up with burnt oil prob caused by high engine temp as radiator was leaking. no previous service history although sticker says cam belt changed at 80k car has done 130k.. battery + side looks like battery has leaked on it a little. don't think that's the cause
but its had a new radiator and people are telling me could be airflow related or egr or maf filter. or even coolant temp sensor.. spend loads on it already any clues ?